Herman Cain on Tuesday vehemently denied all sexual harassment allegations against him and said he had no memory of the first accuser to publicly describe claimed misconduct by the Republican presidential hopeful.

"They simply didn't happen. They simply did not happen," Cain insisted of the accusations of inappropriate sexual behavior, and at least one incident of alleged sexual groping, when he was head of the National Restaurant Association from 1996 to 1999.

But Karen Kraushaar, one of the women who have made allegations, told CNN Tuesday night that Cain is a "serial denier." While declining to comment on Cain's Tuesday remarks, Kraushaar said she wanted to meet with the other accusers about their cases.

At a news conference he held to respond to the latest accusation, made Monday by Sharon Bialek, a Chicago woman who once worked at the restaurant group, Cain described her as a "troubled" woman put up to making false allegations by forces trying to derail his presidential bid.

Cain said it could be the "Democrat machine" behind the allegations but added that he didn't know for sure. He also said he expected further attempts to smear his name and reputation and vowed that he would not be deterred.

"As far as these accusations causing me to back off and maybe withdraw from this presidential primary race? Ain't going to happen," Cain said.

In an earlier interview with ABC News, Cain responded "yes" when asked whether Bialek was lying when she said at a news conference Monday that Cain made an unwanted sexual advance in 1997.

Saying he didn't remember Bialek or the alleged incident, Cain added, "I have absolutely not acted inappropriately with this woman or anyone else in my entire life."

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The latest twist came as more details emerged involving two other former employees at the restaurant association who received payouts and left their jobs, reportedly after accusing Cain of inappropriate behavior.

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In addition, Bennett challenged Cain's contention that he was unable to remember what Kraushaar had accused him of doing 12 years earlier. The restaurant association said at the time that it investigated the accusations and Cain denied them, Bennett noted.

At the news conference, Cain said the only complaint he could recall regarding Kraushaar involved a comment he made that she was about the same height as his wife, as he held his hand up to his chin. He said Kraushaar's complaints had been found to be baseless at the time, and the restaurant association negotiated a severance agreement with her rather than a legal settlement regarding any sexual harassment charges.

Kraushaar told CNN Chief Political Analyst Gloria Borger that the height remark was not the basis for her complaint. And, Kraushaar told CNN, she received a $46,000 sexual harassment settlement, rather than a severance agreement.

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Kraushaar said she would like to organize a joint press conference some time in the near future with some of the other women. "There is safety in numbers," she said. "It is important that it happen in one conference."

Bennett told CNN that Gloria Allred and Bialek have agreed to participate.

Cain was introduced at the news conference by Georgia attorney Lin Wood, who said the candidate is having to respond to hearsay, not admissible evidence, in the "court of public opinion."

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"He comes before you today to defend his reputation," said Wood, who represented vindicated Olympic Park bombing suspect Richard Jewell and John and Patsy Ramsey, parents of child murder victim JonBenet Ramsey. "A reputation that he has built over 40 years of being a good and decent man and a successful business person. I ask you at least afford him fairness."

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Meanwhile, a longtime friend of one of Cain's unidentified accusers said Tuesday that Cain mentioned a possible job promotion at the same time he made the accuser uncomfortable with sexual innuendo and overtures.

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The woman, who spoke on condition of not being identified, said she spoke extensively with her friend about Cain's conduct in 1998 at the time the accuser was allegedly being harassed by Cain while both worked at the restaurant association.

According to the woman, the accuser worked in government relations for the restaurant association in 1998 and told her it was well-known that Cain behaved badly.

Bialek said earlier Tuesday that a reason she came forward with her account of Cain's alleged misbehavior 14 years after the fact was encouragement from her 13-year-old son.

"He said, 'Mom, I think you need to do the right thing. I think you need to tell on him,' " Bialek said on CNN's "American Morning." "That confirmed it for me. If my son is saying it, I want to be the role model for him and other kids growing up."

Bialek's story was the first public, detailed account of alleged misbehavior by Cain. She alleged that Cain groped her following a dinner in 1997, shortly after she was laid off by the restaurant association.

Cain unexpectedly put his hand on her leg beneath her skirt and reached for her genitals and pushed her head toward his crotch after a dinner at which she sought his help finding a job, she said.

Bialek said Cain told her, "You want a job, right?" but stopped when she protested.

"I respected him. I looked up to him. And it just was shocking to me that he would use that power in such a way," Bialek said.

She didn't file a complaint at the time because she no longer worked for the association, said Bialek, who also denied wanting any money for going public, despite a bankruptcy stemming from costs related to her late mother's medical bills.

"The feelings that you have when you know that all of this is totally fabricated: You go from anger, then you get disgusted," he told Kimmel. "There's not an ounce of truth in all of these accusations."

In a written statement, campaign spokesman J.D. Gordon said there was "no record, nor even a complaint filed" to support Bialek's accusation.

Bialek's bombshell came as Cain was in his second week of battling the sexual harassment allegations that have overwhelmed his front-running campaign for the Republican presidential nomination.

Cain has come from far back to join former Massachusetts Gov. Mitt Romney atop the polls, and his campaign said it raised $2 million in the week since the sexual harassment accusations first surfaced in an October 30 report by Politico. By comparison, the campaign raised $2.8 million in the three-month quarter from June through October.

However, Republican Sen. Lisa Murkowski of Alaska said Tuesday that Cain should quit the race if the allegations against him are true.

"It takes incredible courage for an individual to come forward," as Bialek has done, Murkowski said. "So it does cause me to wonder exactly what is out there. I am concerned."

Bialek's fiance, Mark Harwood, backed her up in an interview with CNN affiliate WGN-TV.

"This isn't for fun. You don't go on a political stage and make these kinds of press conferences unless you really stand by your convictions," he said. "There was no money motive to this. She's got the same political interests as Herman Cain in terms of party, so it wasn't like there was opposing political gain here at all."

In denying all the allegations, Cain said Tuesday that he still has the support of his wife of more than 40 years.

"She knows that's not something I would do," he said.

Cain, a favorite of tea party conservatives, has risen to the top of the polls after strong performances in several debates and the release of his "9-9-9" tax plan, which sets flat 9% rates for corporate and income taxes and creates a 9% national sales tax.

He has complained that the sexual harassment allegations amount to a baseless media onslaught against his campaign.

Several unaffiliated Republican operatives said Cain must say more about the allegations, because his current message is not putting the controversy to rest.

"He needs to be upfront, forthright and get this story behind him," said Bob Vander Plaats, a leading Iowa Republican activist. The ongoing allegations, he adds, are a "test of Cain's leadership" and "a tipping point for his campaign."

Cain will be in Iowa on November 19 for an event sponsored by Vander Plaats called the Family Leader Forum. An expected 2,500 potential caucus-goers will be in attendance, and Cain will probably have to address the issue in some form.

"You cannot let this dominate the campaign," Vander Plaats said, a sentiment echoed by other analysts. He said Cain can "approach this with humility and sincerity" and people will listen. "Iowans are fair."

Allred said her client is a registered Republican and described Cain's behavior at the time to her then-boyfriend and a longtime mentor. Both have given sworn statements supporting her account, Allred said. She told CNN Tuesday that Cain and the women should testify under oath.